Though it's possible that they were both exposed to something in the environment that resulting in an allergic reaction, the situation sounds more like a type of viral rash that one got from the other. There are a variety of viral skin rashes that children get, but they rarely require urgent medical treatment, especially when there are no other symptoms like high fever, vomiting, chills, or trouble breathing. These generic viral rashes can have many different appearances, and be accompanied by some other mild symptoms, but again, as long as neither of your children feel especially ill, they will likely resolve on their own. Among various generic viral causes, Fifth Disease came to mind from your description, which is a common childhood skin rash that can affect the trunk and extremities, and is caused by the parvovirus. None of these causes are typically cause for any worry, and as you've already begun to notice, they will go away in several days (to weeks).
Though treatment isn't required, if either child is uncomfortable from itching, you can continue giving an over-the-counter anti-histamine like benadryl, or apply a hydrocortisone steroid cream (also OTC). Be sure to give them plenty of fluids to aid in recovery from the infection and prevent dehydration, and they'll be back to their usual, rambunctious selves in no time.
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I hope this helps!